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**Register Transfer and Microoperations Part2**

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**4.5 Logic Microoperations**

Manipulating the bits stored in a register Logic Microoperations 2

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**Clear Logic operation can…**

clear a group of bit values (Anding the bits to be cleared with zeros) R1 (data) R2 (mask) R1

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Set set a group of bit values (Oring the bits to be set to ones with ones) R1 (data) R2 (mask) R1

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Complement Complement a group of bit values (Exclusively Or (XOR) the bits to be complemented with ones) R1 (data) R2 (mask) R1

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LOGIC CIRCUIT • A variety of logic gates are inserted for each bit of registers. Different bitwise logical operations are selected by select signals. 6

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Example Extend the previous logic circuit to accommodate XNOR, NAND, NOR, and the complement of the second input. S2 S1 S0 Output Operation X Y AND 1 X Y OR X Å Y XOR A Complement A (X Y) NAND (X Y) NOR (X Å Y) XNOR B Complement B 7

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**More Logic Microoperation**

X Y F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14 F15 TABLE Truth Table for 16 Functions of Two Variables Boolean function Microoperation Name F0 = F ← Clear F1 = xy F ← A∧B AND F2 = xy’ F ← A∧B F3 = x F ← A Transfer A F4 = x’y F ← A∧B F5 = y F ← B Transfer B F6 = x y F ← A B Ex-OR F7 = x+y F ← A∨B OR Boolean function Microoperation Name F8 = (x+y)’ F ← A∨B NOR F9 = (x y)’ F ← A B Ex-NOR F10 = y’ F ← B Compl-B F11 = x+y’ F ← A∨B F12 = x’ F ← A Compl-A F13 = x’+y F ← A∨B F14 = (xy)’ F ← A∧B NAND F15 = F ← all 1’s set to all 1’s TABLE Sixteen Logic Microoperations 8

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Insert Insert The insert operation inserts a new value into a group of bits This is done by first masking the bits and then ORing them with the required value 1) Mask ) OR A before A before B mask B insert A after mask A B A after insert AVB

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**4-6 Shift Microoperations**

Shift example: Shift Microoperations : Shift microoperations are used for serial transfer of data Three types of shift microoperation : Logical, Circular, and Arithmetic

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**Shift Microoperations**

Symbolic designation Description R ← shl R Shift-left register R R ← shr R Shift-right register R R ← cil R Circular shift-left register R R ← cir R Circular shift-right register R R ← ashl R Arithmetic shift-left R R ← ashr R Arithmetic shift-right R TABLE Shift Microoperations

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**Logical Shift A logical shift transfers 0 through the serial input**

The bit transferred to the end position through the serial input is assumed to be 0 during a logical shift (Zero inserted)

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Logical Shift Example 1. Logical shift: Transfers 0 through the serial input. R1 ¬ shl R1 Logical shift-left R2 ¬ shr R2 Logical shift-right (Example) Logical shift-left

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Circular Shift The circular shift circulates the bits of the register around the two ends without loss of information

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**Circular Shift Example**

Circular shift-left Circular shift-right (Example) Circular shift-left is shifted to

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Arithmetic Shift An arithmetic shift shifts a signed binary number to the left or right An arithmetic shift-left multiplies a signed binary number by 2 An arithmetic shift-right divides the number by 2 In arithmetic shifts the sign bit receives a special treatment

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**Arithmetic Shift Right**

Arithmetic right-shift: Rn-1 remains unchanged; Rn-2 receives Rn-1, Rn-3 receives Rn-2, so on. For a negative number, 1 is shifted from the sign bit to the right. A negative number is represented by the 2’s complement. The sign bit remained unchanged.

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**Arithmetic Shift Right**

Example 1 0100 (4) 0010 (2) Example 2 1010 (-6) 1101 (-3)

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**Arithmetic Shift Left The operation is same with Logic shift-left**

The only difference is you need to check overflow problem Carry out Sign bit LSB LSB Rn-1 Rn-2 0 insert Vs=1 : Overflow Vs=0 : use sign bit

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**Arithmetic Shift Left Arithmetic Shift Left : 0010 (2) 0100 (4)**

Example 1 0010 (2) 0100 (4) Example 2 1110 (-2) 1100 (-4)

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**Arithmetic Shift Left Arithmetic Shift Left : 0100 (4) **

Example 3 0100 (4) 1000 (overflow) Example 4 1010 (-6) 0100 (overflow)

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Lecture 6 More Logic Functions: NAND, NOR, XOR and XNOR

Lecture 6 More Logic Functions: NAND, NOR, XOR and XNOR

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